Can I overclock my Intel HD integrated GPU that supports OpenGL 2.1 to support OpenGL 3.0, or even better, 3.2? If this can be done, can you recommend me a tutorial?
Overclocking is the action of raising the frequency of a clock (an electronic circuit that emits signals at regular intervals that are used as reference by other electronic circuits in a given device to synchronize with each other) in a device by various means such as changing a built-in setting, raising the voltage, etc.
Overclocking can't give a finished product features it didn't have when it left the factory.
OpenGL is an API between the application and the graphics driver. Therefore OpenGL support is determined more by the driver than by the hardware. Even if a card does not offer acceleration for some of the newer OpenGL procedures, they can be emulated in software. Taking it to extreme, it is even possible to run OpenGL 3.2 on plain CPU (software renderer), it would be only a little slower.
Therefore I recommending just installing more up-to-date driver first and it might solve your problem.
BTW, recently I had my hardware acceleration accidentally disabled and I didn't notice any performance drop in desktop behavior, only the laptop battery life suffered and CPU was going up to 20-30% during animated desktop window actions or activating 3D window switcher, etc.